[PDF] Top 20 The edge tenacity of a split graph

... of tenacity of a graph G was introduced in [2,3], as a useful measure of the ”vulnerability” of ...that tenacity is a most suitable measure of stability or vulnerability in that for many graphs it is ... See full document

... We consider only finite undirected graphs without loops and multiple edges. Our ter- minology will be standard except as indicated; a good reference for any undefined terms is [1]. Throughout the paper G = (V, E) will ... See full document

... In this paper, we will consider only simple, undirected and finite graphs, i.e., undirected graphs on a finite number of vertices without multiple edges or loops. Let Γ = (V, E) be a graph with vertex set V and ... See full document

... a graph G, ...simple graph G (without loops or multiple edges) is the minimum number of vertices whose removal results in a disconnected graph or results in the trivial graph K 1 .... ... See full document

... In this paper, we consider the rainbow number of cycles. Erd˝os et al. [3] posed a conjecture on the anti-Ramsey number for cycles in complete graphs, which was later proved by Montellano et al. [8]. Axenovich et al. [1] ... See full document

... The metric dimension problem is an application to network discovery and verification in the area of the telecommunication. Due to its fast dynamics, distributed growth process, it is hard to obtain an accurate map of the ... See full document

... for split graphs. It follows that a connected graph is 1-critical in respect of its CHP and CHI in that the addition (or deletion) of a vertex (or vertices) or the addition (or deletion) of an edge ... See full document

... A dominating set D V is said to be a split dominating set of G , if the induced sub graph V  D is disconnected. The minimum cardinality of vertices in such a set is called the split domination ... See full document

... environment. Graph tenacity has been an active area of research since the the concept was introduced in ...the tenacity,T(G), and the Mix-tenacity, T m (G), of a ... See full document

... A graph G is called an edge detour graph if it has an edge detour ...set. Edge detour graphs were introduced and studied in [7]. A split (G,D)-set S of a graph G is said ... See full document

... number of vertices whose removal results in a disconnected graph. A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to atleast one vertex in S. The minimum cardinality taken over ... See full document

... the edge 𝑥 𝑖𝑘 such that 𝜇(𝑥 𝑖𝑘 ) = 𝜎 𝑠 (𝑢 𝑖 ), 1 ≤ 𝑘 ≤ 𝑛 ...any edge in 𝐸(𝐺) − 𝐷 ′ ...the edge 𝑥 𝑖𝑘 in 𝐷 ′ for some i. That is the edge x is dominated by the edge 𝑥 𝑖𝑘 ...an edge ... See full document

... a graph, and let g be a function that assigns to each edge a set of colors chosen from the power set of {1,2} that is, g:E(G)→ ...each edge E(G) such that g( we have ⋃ = {1,2}, then g is called ... See full document

... Graph colorings is one of the most important concepts in graph theory. In the present paper we study the existence of a Hamilton cycle with many colors, also the existence of a Hamilton cycle with few ... See full document

... 1. Suppose f is an isolated edge of G . Let F be any minimum EED set of G . Then f ∈ F . Let F 1 = F \ { } f . Now consider the subgraph G \ f . Let h be any edge of G \ f such that h does not belongs to F ... See full document

... of graph theory. The graph theory is a very useful tool for solving combinatorial problems in different areas such as operations research, optimization, topology, geometry, number theory, algebra and ... See full document

... fuzzy graph G : (σ, μ) is a pair of functions (σ, μ) , where σ : V →[0,1] is a fuzzy subset of a non empty set V and μ : V × V →[0, 1] is a symmetric fuzzy relation on σ such that for all u, v in V , the relation ... See full document

...       , a contradiction. Thus S does not con- tain any edge of N(e). Since   ( G e   )   ( ) G  1 , is a γ'-set of G and so Equation (1) holds. Conversely, suppose e is an edge such that (1) is ... See full document

... Flower graph Fl16 : {-10,-6,-9, -7,-8,8,9,7,10,6,-5,-11,5,11,14,12,13,-13,-14,-12} A Q(6)-BEM labeling for Flower graph Fl16 : {-10,-6,-9, -7,-8,8,9,7,10,6,-15,-15,11,14,12,13, -13,-14,-12,-11} A Q(7)-BEM ... See full document

... Swaminathanet al[13] introduced the concept of equitable domination in graphs, by considering the following real world problems like : in a network nodes with nearly equal capacity may interact with each other in a ... See full document